Complexes of type C6H7(+)·L (L = N2 and CO2) studied by explicitly correlated coupled cluster theory

Complexes of the benzenium ion (C(6)H(7)(+)) with N(2) or CO(2) have been studied by explicitly correlated coupled cluster theory at the CCSD(T)-F12x (x = a, b) level [T. B. Adler et al., J. Chem. Phys. 127, 221106 (2007)] and the double-hybrid density functional B2PLYP-D [T. Schwabe and S. Grimme, Phys. Chem. Chem. Phys. 9, 3397 (2007)]. Improved harmonic vibrational wavenumbers for C(6)H(7)(+) have been obtained by CCSD(T?)-F12a calculations with the VTZ-F12 basis set. Combining them with previous B2PLYP-D anharmonic contributions we arrive at anharmonic wavenumbers which are in excellent agreement with recent experimental data from p-H(2) matrix isolation IR spectroscopy [M. Bahou et al., J. Chem. Phys. 136, 154304 (2012)]. The energetically most favourable conformer of C(6)H(7)(+)·N(2) shows a π-bonded structure similar to C(6)H(7)(+)·Rg (Rg = Ne, Ar) [P. Botschwina and R. Oswald, J. Phys. Chem. A 115, 13664 (2011)] with D(e) ≈ 870 cm(-1). For C(6)H(7)(+)·CO(2), a slightly lower energy is calculated for a conformer with the CO(2) ligand lying in the ring-plane of the C(6)H(7)(+) moiety (D(e) ≈ 1508 cm(-1)). It may be discriminated from other conformers through a strong band predicted at 1218 cm(-1), red-shifted by 21 cm(-1) from the corresponding band of free C(6)H(7)(+).     

Remarks on Multilevel Bases for Divergence-Free Finite Elements

The connection between the multilevel factorization method recently proposed by Sarin and Sameh for solving mixed discretizations of the Stokes equation using a divergence-free finite element formulation, and hierarchical basis preconditioners for the Poisson problem is established. For the 2D triangular Taylor–Hood element, a preconditioner is proposed that could be useful in fractional step methods.     

3β‐Acetoxy‐5α,6β‐di­hydroxybisnorcholanic acid 2216 lactone

In the title compound, C₂₄H₃₆O₆, the ester linkage in ring A is equatorial. The six‐membered rings A, B and C have chair conformations. The five‐membered ring D adopts a 13β,14α‐half‐chair conformation and the E ring adopts an envelope conformation. The A/B, B/C and C/D ring junctions are trans, whereas the D/E junction is cis.     

Characterization of thin Ta-Si-Nx layers of different nitrogen content using XPS, UPS and STM

Reactively sputtered Ta-Si-N_x barrier systems of different nitrogen content on copper were investigated by photoelectron spectroscopy (XPS, UPS) and scanning tunnelling microscopy (STM). The measured photoelectron spectra (excitation He-I) showed a clear dependence of the electron state density near the Fermi edge on the content of nitrogen. These results correlate with the I(U) characteristics of the STM measurements and the electrical conductivity of these layers.     

Optimality of multilevel preconditioning for nonconforming P1 finite elements

We prove the optimality of hierarchical and BPX-type preconditioners for finite element discretizations with nonconforming P1 finite elements. Such preconditioners were proposed about 15 years ago, and until now only suboptimal estimates of their preconditioning properties have been available. The main new tool is an improved Bernstein type inequality for an associated subdivision process generated by the prolongations which allows us to give an asymptotically optimal upper bound for the spectrum of the preconditioned systems.     

Luminescence of Pr,Nd and Yb ions implanted in GaAs and GaP

New experimental data on luminescence spectra of Pr and Nd ions implanted into GaAs and GaP crystals and the results on luminescence kinetics of Nd doped GaP are presented. The results show that RE ions form different complexes in measured samples.     

Generators of the unoriented bordism ring which are fibered over products of projective spacesRP(2 r −1)

For each positive integerk≦∞ we construct a family {M _k ⁿ } of generators of the unoriented bordims ring. The manifoldsM _k ⁿ are total spaces of fiber bundles whose base spaces are high-dimensional products of projective spaces wherer _i≦k. The fibers are themselves iterated projective bundles with maximal fiber dimension two. In the special casek=3 we obtain generatorsM ₃ ⁿ which admit approximately 7/8·n pointwise linearly independent vector fields. This article was processed by the author using the LAT_EX style filecljour1 from Springer-Verlag     

Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems

We describe tensor product type techniques to derive robust solvers for anisotropic elliptic model problems on rectangular domains in ^d . Our analysis is based on the theory of additive subspace correction methods and applies to finite element and prewavelet schemes. We present multilevel- and prewavelet-based methods that are robust for anisotropic diffusion operators with additional Helmholtz term. Furthermore, the resulting convergence rates are independent of the discretization level. Beside their theoretical foundation, we also report on the results of various numerical experiments to compare the different methods.